The inverse moment problem for convex polytopes

The goal of this paper is to present a general and novel approach for the reconstruction of any convex d-dimensional polytope P, from knowledge of its moments. In particular, we show that the vertices of an N-vertex polytope in R^d can be reconstructed from the knowledge of O(DN) axial moments (w.r.t. to an unknown polynomial measure od degree D) in d+1 distinct generic directions. Our approach is based on the collection of moment formulas due to Brion, Lawrence, Khovanskii-Pukhikov, and Barvinok that arise in the discrete geometry of polytopes, and what variously known as Prony's method, or Vandermonde factorization of finite rank Hankel matrices.Comment: LaTeX2e, 24 pages including 1 appendi

Unfolding Rates for the Diffusion-Collision Model

In the diffusion-collision model, the unfolding rates are given by the likelihood of secondary structural cluster dissociation. In this work, we introduce an unfolding rate calculation for proteins whose secondary structural elements are $\alpha$-helices, modeled from thermal escape over a barrier which arises from the free energy in buried hydrophobic residues. Our results are in good agreement with currently accepted values for the attempt rate.Comment: Shorter version of cond-mat/0011024 accepted for publication in PR

Entropic Interactions in Suspensions of Semi-Flexible Rods: Short-Range Effects of Flexibility

We compute the entropic interactions between two colloidal spheres immersed in a dilute suspension of semi-flexible rods. Our model treats the semi-flexible rod as a bent rod at fixed angle, set by the rod contour and persistence lengths. The entropic forces arising from this additional rotational degree of freedom are captured quantitatively by the model, and account for observations at short range in a recent experiment. Global fits to the interaction potential data suggest the persistence length of fd-virus is about two to three times smaller than the commonly used value of $2.2 \mu {m}$.Comment: 4 pages, 5 figures, submitted to PRE rapid communication

Presidential Popularity and Reputation

This paper reports on the results of an empirical study of relationships between the popularity of US presidents and economic variables. Traditionally, these relationships are based on the hypothesis that voters hold the incumbent President responsible for the economic situation. We derive an alternative specification of popularity, based on the hypothesis that political parties perform better on different issues. Empirical evidence turns out to be strongly in favour of our hypothesis. Our findings have important implications for studies on government behaviour in which it is assumed that one of the objectives of administrations is to maximise votes

The Physics of turbulent and dynamically unstable Herbig-Haro jets

The overall properties of the Herbig-Haro objects such as centerline velocity, transversal profile of velocity, flow of mass and energy are explained adopting two models for the turbulent jet. The complex shapes of the Herbig-Haro objects, such as the arc in HH34 can be explained introducing the combination of different kinematic effects such as velocity behavior along the main direction of the jet and the velocity of the star in the interstellar medium. The behavior of the intensity or brightness of the line of emission is explored in three different cases : transversal 1D cut, longitudinal 1D cut and 2D map. An analytical explanation for the enhancement in intensity or brightness such as usually modeled by the bow shock is given by a careful analysis of the geometrical properties of the torus.Comment: 17 pages, 10 figures. Accepted for publication in Astrophysics & Spac

Global Reconstruction of Naturalized River Flows at 2.94 Million Reaches

Spatiotemporally continuous global river discharge estimates across the full spectrum of stream orders are vital to a range of hydrologic applications, yet they remain poorly constrained. Here we present a carefully designed modeling effort (Variable Infiltration Capacity land surface model and Routing Application for Parallel computatIon of Discharge river routing model) to estimate global river discharge at very high resolutions. The precipitation forcing is from a recently published 0.1° global product that optimally merged gauge-, reanalysis-, and satellite-based data. To constrain runoff simulations, we use a set of machine learning-derived, global runoff characteristics maps (i.e., runoff at various exceedance probability percentiles) for grid-by-grid model calibration and bias correction. To support spaceborne discharge studies, the river flowlines are defined at their true geometry and location as much as possible—approximately 2.94 million vector flowlines (median length 6.8 km) and unit catchments are derived from a high-accuracy global digital elevation model at 3-arcsec resolution (~90 m), which serves as the underlying hydrography for river routing. Our 35-year daily and monthly model simulations are evaluated against over 14,000 gauges globally. Among them, 35% (64%) have a percentage bias within ±20% (±50%), and 29% (62%) have a monthly Kling-Gupta Efficiency ≥0.6 (0.2), showing data robustness at the scale the model is assessed. This reconstructed discharge record can be used as a priori information for the Surface Water and Ocean Topography satellite mission's discharge product, thus named “Global Reach-level A priori Discharge Estimates for Surface Water and Ocean Topography”. It can also be used in other hydrologic applications requiring spatially explicit estimates of global river flows

The <i>Castalia</i> mission to Main Belt Comet 133P/Elst-Pizarro

We describe Castalia, a proposed mission to rendezvous with a Main Belt Comet (MBC), 133P/Elst-Pizarro. MBCs are a recently discovered population of apparently icy bodies within the main asteroid belt between Mars and Jupiter, which may represent the remnants of the population which supplied the early Earth with water. Castalia will perform the first exploration of this population by characterising 133P in detail, solving the puzzle of the MBC’s activity, and making the first in situ measurements of water in the asteroid belt. In many ways a successor to ESA’s highly successful Rosetta mission, Castalia will allow direct comparison between very different classes of comet, including measuring critical isotope ratios, plasma and dust properties. It will also feature the first radar system to visit a minor body, mapping the ice in the interior. Castalia was proposed, in slightly different versions, to the ESA M4 and M5 calls within the Cosmic Vision programme. We describe the science motivation for the mission, the measurements required to achieve the scientific goals, and the proposed instrument payload and spacecraft to achieve these

Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem